Electrons moving in a periodic electric potential form Bloch energy
bands where the mass of electrons are effectively changed. In a strong
magnetic field, the cyclotron orbits of free electrons are quantized and
Landau levels forms with a massive degeneracy within. In 1976,
Hofstadter showed that for 2-dimensional electronic system, the
intriguing interplay between these two quantization effects can lead
into a self-similar fractal set of energy spectrum known as